Visual explanations of machine learning model estimating charge states in quantum dots Yui Muto1 2Takumi Nakaso3Motoya Shinozaki4Takumi Aizawa1 2Takahito

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Visual explanations of machine learning model estimating charge states in

quantum dots

Yui Muto,1, 2 Takumi Nakaso,3Motoya Shinozaki,4Takumi Aizawa,1, 2 Takahito

Kitada,1, 2 Takashi Nakajima,5Matthieu R. Delbecq,5Jun Yoneda,5Kenta

Takeda,5Akito Noiri,5Arne Ludwig,6Andreas D. Wieck,6Seigo Tarucha,5

Atsunori Kanemura,3Motoki Shiga,7, 8, 9 and Tomohiro Otsuka4, 1, 2, 10, 5, ∗

1Research Institute of Electrical Communication, Tohoku University,

2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

2Department of Electronic Engineering,

Graduate School of Engineering, Tohoku University,

Aoba 6-6-05, Aramaki, Aoba-Ku, Sendai 980-8579, Japan

3LeapMind, 28-1 Maruyama-cho, Shibuya-ku, Tokyo 150-0044, Japan

4WPI Advanced Institute for Materials Research, Tohoku University,

2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

5Center for Emergent Matter Science, RIKEN,

2-1 Hirosawa, Wako, Saitama 351-0198, Japan

6Ruhr University, Bochum, Universit¨

atsstraße 150, 44801 Bochum, German

7Unprecedented-scale Data Analytics Center, Tohoku University,

6-3 Aoba, Aramakiaza, Aoba-ku, Sendai, 980-8578 Japan

8RIKEN Center for Advanced Intelligence Project,

1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan

9Graduate School of Information Science, Tohoku University,

6-3-09 Aoba, Aramaki-aza Aoba-ku, Sendai, 980-8579, Japan

10Center for Science and Innovation in Spintronics,

Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

(Dated: December 29, 2023)

arXiv:2210.15070v2 [cond-mat.mes-hall] 27 Dec 2023

Abstract

Charge state recognition in quantum dot devices is important in the preparation of quantum bits for

quantum information processing. Toward auto-tuning of larger-scale quantum devices, automatic charge

state recognition by machine learning has been demonstrated. For further development of this technology,

an understanding of the operation of the machine learning model, which is usually a black box, will be

useful. In this study, we analyze the explainability of the machine learning model estimating charge states in

quantum dots by gradient-weighted class activation mapping, which identiﬁed class-discriminative regions

for the predictions. The model predicts the state based on the change transition lines, indicating that human-

like recognition is realized. We also demonstrate improvements of the model by utilizing feedback from the

mapping results. Due to the simplicity of our simulation and pre-processing methods, our approach offers

scalability without signiﬁcant additional simulation costs, demonstrating its suitability for future quantum

dot system expansions.

INTRODUCTION

Semiconductor quantum bits (qubits) that utilize electron spins in semiconductor quantum

dots are expected to be good candidates for future qubits because of their high operation ﬁ-

delity and excellent integration properties. Basic operations such as single-qubit[1,2] and two-

qubit operations[3,4] have been demonstrated, and quantum error correction has also been

demonstrated[12] with improved operation ﬁdelity[5–11]. Furthermore, attempts are being made

to construct large-scale quantum systems using semiconductor integration technology[13–20]. It

is essential to trap one electron in each quantum dot to construct semiconductor qubits. Charge

state tuning in semiconductor quantum dot devices is required for this purpose. In previous exper-

iments, this has been mainly accomplished by manually adjusting the gate voltages to achieve the

desired charge states. However, this approach requires a signiﬁcant amount of time to learn and

execute. This will make tuning large-scale semiconductor quantum systems difﬁcult in the future.

There is a movement to solve such a difﬁcult problem automatically[21]. The main types

of algorithms studied in these methods are script-based algorithms[24–27] or machine-learning

(ML) methods[28–39]. In particular, ML methods are expected to be more easily applicable to

different experimental environments and more compatible with different devices. Efforts to de-

velop ML methods for auto-tuning quantum device parameters are currently underway [22,23].

In ML methods, the amount of labeled data required for network training is enormous, making

the preparation of labeled experimental data as training data a labor-intensive task. Consequently,

simulations have been utilized to generate training data. This approach has led to the develop-

ment of a method that utilizes the Thomas-Fermi model and deep convolutional neural networks

(CNN) for recognizing charge states [28]. Also, by adding various types of noise that could be

observed in real experiments to the training data, the noise-robust charge states recognition has

been demonstrated [39].

Thus far, charge state recognition has primarily been demonstrated in double quantum dots [28,

31,39]. Looking towards the future large-scale integration of quantum dots, there is a need to

explore scalable methods. Also, while the Thomas-Fermi model with added noise is highly useful

as a physical model, the necessity of such physical accuracy in a data generation model for machine

learning has not been extensively debated. For instance, humans tend to estimate charge states

by focusing mainly on charge transition lines, without giving much consideration to background

noise. Therefore, generating training data with a physical model that reﬂects these characteristics

could lead to the realization of an estimator with judgment criteria similar to those of humans.

Such an estimator would likely be more user-friendly for humans, as it would share the same

criteria for judgment. To achieve this, it is important to clarify the criteria for judgment, which is

usually a black box.

In this study, we analyze the operation of the ML model that estimates the charge states in

double quantum dots. We propose pre-processing the data through binarization, which enables

us to use a simple simulation model to generate training data. We also visualize the interest of

the model by gradient-weighted class activation mapping (Grad-CAM) [40] and conﬁrm that they

are on the charge transition lines. By incorporating feedback from the Grad-CAM results, we

demonstrate improvements in the ML model.

PREPARATION OF THE CHARGE STATE ESTIMATOR

Figure 1(a) illustrates the process ﬂow for generating a charge state estimator (CSE). Initially,

the preparation of training data is needed to train the ML model. We utilize a constant interac-

tion (CI) model in the simulation for simplicity, where quantum dots are modeled as a capacitor

circuit[41,42]. Using this CI model and treating the electrostatic coupling between the double

quantum dot and the charge sensor, we can obtain the charge stability diagrams with the size

(30×30) pixel measured using a charge sensor by changing the parameters in the model. This size

is chosen to achieve a sufﬁcient resolution to distinguish the charge transition lines. The next step

is to prepare the charge state label: no quantum dot (ND), left (LD), center (CD), right (RD), or

double quantum dot (DD), for each stability diagram (Fig. 1(a) step 0). Note that the CD state is

formed by strong coupling between both dot sites, which in the CI model is expressed by setting a

large value for Cm. Here, the diagrams are automatically categorized based on the largest number

of quantum dots in the region.

Next, pre-processing is performed on these images. All images are differentiated in the x-axis

to make the charge transition lines clear (Fig. 1(a) step 1). Then, the images are binarized by

adaptive thresholding to simplify them into black and white images (Fig. 1(a) step 2). Here, the

charge transition line is set to white, while the background is set to black. In this process, we use

Adaptive Thresholding by the OpenCV module [43].

To adapt to noisy experimental data, random noise is added to these images. Due to binarization

in the previous step, noise can be realized by simply ﬂipping the black and white pixel values at

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VisualexplanationsofmachinelearningmodelestimatingchargestatesinquantumdotsYuiMuto,1,2TakumiNakaso,3MotoyaShinozaki,4TakumiAizawa,1,2TakahitoKitada,1,2TakashiNakajima,5MatthieuR.Delbecq,5JunYoneda,5KentaTakeda,5AkitoNoiri,5ArneLudwig,6AndreasD.Wieck,6SeigoTarucha,5AtsunoriKanemura,3MotokiShiga,7,8,9...

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Visual explanations of machine learning model estimating charge states in quantum dots Yui Muto1 2Takumi Nakaso3Motoya Shinozaki4Takumi Aizawa1 2Takahito

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